A three dimensional inverse scattering algorithm in the time-domain based on nonlinear optimization

A new algorithm for solving the three-dimensional inverse scattering problem using time-domain data is presented. The algorithm is intended for application in cases where linearization using the Born or Rytov approximations is not possible. A functional is defined accounting for the error of the object and data equations and the unknown coefficients of the internal field and the object function are sought in order to minimize it. The algorithm projects the unknown internal field into a space of Gaussian basis functions aiming to decrease the number of the unknown coefficients. Time-windowing is utilized in order to reduce the size of the optimization problem.